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    Title: 一些Hadamard不等式的推廣與更細緻的結果
    Other Titles: On some generalizations and refinements of Hadamard's inequality
    Authors: 王嘉鈴;Wang, Jia-Ling
    Contributors: 淡江大學中等學校教師在職進修數學教學碩士學位班
    楊國勝;Yang, Gou-Sheng
    Keywords: Hadamard不等式;凸函數;Hadamard's double inequality;convex functions
    Date: 2014
    Issue Date: 2015-05-04 09:48:53 (UTC+8)
    Abstract: 設 f:I⊆R→R 為凸函數(convex function) ,其中a,b ϵ I , a<b,則下列不等式恆成立
    f((a+b)/2)≤1/(b-a) ∫_a^b▒f(x) dx ≤1/2 [f(a)+f(b)] (1.1)
    此為廣為人知的Hadamard雙邊不等式。
    本文試著就此Hadamard雙邊不等式(1.1),建立一些推廣與更細緻的結果。
    the following double inequality
    f((a+b)/2)≤1/(b-a) ∫_a^b▒f(x) dx≤1/2 [f(a)+f(b)] (1.1)
    holds for all convex function on [a, b] is known in the literature as Hermite-Hadamard (or Hadamard ) inequality.
    The main purpose of this paper is to establish some generalizations and refinements of the inequality (1.1).
    Appears in Collections:[數學學系暨研究所] 學位論文

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